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dalvyx
6 days ago
14

A wind turbine with a rotor diameter of 40 m produces 90 kW of electrical power when the wind speed is 8 m/s. The density of air

impinging on the turbine is 1.2 kg/m3. What fraction of the kinetic energy of the wind impinging on the turbine is converted to electrical energy
Physics
1 answer:
Softa [2.9K]6 days ago
8 0
0.233. Explanation: Given that the diameter of the rotor is d = 40 m, Power P = 90 kW, Wind speed v = 8 m/s, and Air density ρ = 1.2 kg/m³. It is established that KE = ½mv², where mass flow rate m = ρAv, with Area A = πd²/4. Thus, A = (3.142 * 40²)/4, resulting in A = 1256.8 m². Substituting A into the mass flow rate equation gives m = 1.2 * 1256.8 * 8 = 12065.28. Substituting m into the KE equation yields KE = ½ * 12065.28 * 8² = 386.1 kW. The fraction of kinetic energy converted to electric energy is Fraction = Electric Power / Total KE = 90 / 386.1 = 0.233.
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